But luckily for us, there's a classical equation of motion that will, in fact, describe how the electron and nucleus change position or change their radius as a function of time.

但幸运的是，有一个,经典方程描述了电子和核子,位置或者它们直接的距离是,如何随时间变化的。

麻省理工公开课 - 化学原理课程节选

It's somewhat different when we're talking about the p or the d orbitals, and we won't go into the equation there, but this will give you an idea of what we're really talking about with this radial probability distribution.

当我们讨论ｐ轨道或者,ｄ轨道的时候会有些不同，我们那时不会给出方程，但它会给你们一个,关于径向概率,分布的概念。

麻省理工公开课 - 化学原理课程节选

Or, if we know the equation of state from a model, ideal gas, van der Waal's gas, whatever, u now we can determine u.

或者如果我们知道模型的状态方程,比如理想气体，范德瓦尔斯气体，无论什么，我们就可以利用状态方程得到内能。

麻省理工公开课 - 热力学与动力学课程节选

And so a person is just a P-functioning body, whether you emphasize the body side there or the personality side of that equation.

人就是有着人格功能的肉体，无论强调人格部分还是肉体部分。

耶鲁公开课 - 死亡课程节选

You'd pull out your pencil and paper, you can do it as a matrix inversion if you know how to do that, or you can just simply do substitution of one equation into another to solve it.

你知道你在小学的时候是怎么做的对吧？,你拿出你的笔和纸,如果你会的话,你可以解一个方程组,或者你可以单纯地。

麻省理工公开课 - 计算机科学及编程导论课程节选

Some will be growing very rapidly, some will be growing less rapidly, and what this equation shows you here or that rate of growth the to the doubling time of cells.

有些会生长得更快些,有的慢一些,而这个方程告诉你,即生长的速率和细胞倍增的时间联系起来

耶鲁公开课 - 生物医学工程探索课程节选

You can go ahead and use that equation, or you could figure it out every time, because if you know the total number of nodes, and you know the angular node number, then you know how many nodes you're going to have left.

你们可以直接用这个方程，或者每次都自己算出来，因为如果你们知道了总的节点数，又知道角向节点数，就知道剩下的节点数是多少。

麻省理工公开课 - 化学原理课程节选

So we can use an equation to relate the incident energy and the kinetic energy to the ionization energy, or the energy that's required to eject an electron.

因此我们可以用一个公式将入射能量,与动能和电离能，就是发射出一个电子所需要的能量关联起来。

麻省理工公开课 - 化学原理课程节选

So from measured equation of state data, or from a model like the ideal gas or the van der Waal's gas or another equation of state you know this.

所以，从测量的到的状态方程的数据，或者从状态方程模型比如理想气体方程,范德瓦尔斯方程或者其他状态方程,我们就可以知道。

麻省理工公开课 - 热力学与动力学课程节选

And we also, when we solved or we looked at the solution to that Schrodinger equation, what we saw was that we actually needed three different quantum numbers to fully describe the wave function of a hydrogen atom or to fully describe an orbital.

此外，当我们解波函数,或者考虑薛定谔方程的结果时，我们看到的确３个不同的量子数,完全刻画了氢原子,的波函数或者说轨道。

麻省理工公开课 - 化学原理课程节选

So, what we say here is we need to take a step back here and come up with an approximation that's going to allow us to think about using the Schrodinger equation when we're not just talking about hydrogen or one electron, but when we have these multi-electron atoms.

所有我们这里要说的是,我们需要退回一步,做一个近似,那样可以使我们用,薛定谔方程来考虑,让我们不是仅仅在讨论氢原子或者,一个电子的时候，而是多个电子的原子。

麻省理工公开课 - 化学原理课程节选

We can also talk about it in terms of if we want to solve, if we, for example, we want to find out what that initial energy was, we can just rearrange our equation, or we can look at this here where the initial energy is equal to kinetic energy plus the work function.

初始能量是多少，也可以,写成另一种形式,我们可以把方程变形,或者我们看这里,初始能量等于,动能加功函数。

麻省理工公开课 - 化学原理课程节选

So you don't want to put in a negative energy, that's not going to help you out, you need to put in positive energy to get an electron out of the system. So that's why you'll find binding energies are always negative, and ionization energies are always going to be positive, or you could look at the equation and see it from there as well.

因为这对电离没有帮助,你需要一个正的能量,使得电子脱离这个系统,这就是为什么你会发现,结合能总是负的而电离能总是正的,或者你们看这个方程也可以发现这一点。

麻省理工公开课 - 化学原理课程节选

So we'd really like to be able to find some sort of equation of state, or some sort of rather function of state that's going to relate the heat going in or out of the system with that function of state, because this isn't going to do it.

所以我们真的想要去,找到一些态方程或者态函数,通过这个态函数可以表示热量,在系统与外界的交换,因为这个不能表示它。

麻省理工公开课 - 热力学与动力学课程节选

We don't always want to go and solve the Schrodinger equation, and in fact, once we start talking about molecules, I can imagine none of you, as much as you love math or physics, want to be trying to solve this Schrodinger equation in that case either. So, what Lewis structures allow us to do is over 90% of the time be correct in terms of figuring out what the electron configuration is.

我们并不想每次都去解薛定谔方程，而且实际上，一旦我们开始讨论分子，我可以想象,你们中没有一个人，不管你有多么热爱数学或物理，会想去解这种情况下的薛定谔方程,总之，路易斯结构能让我们,有超过，90%，的概率判断出正确的,电子排布。

麻省理工公开课 - 化学原理课程节选